Existence and asymptotic properties of solutions for a nonlinear Schrödinger elliptic equation from geophysical fluid flows

In this paper, we study the existence and asymptotic behavior of radial solutions for a class of nonlinear Schrödinger elliptic equations on infinite domains describing the gyre of geophysical fluid flows. The existence theorem and asymptotic properties of radial positive solutions are established by using a new renormalization technique.     

The maximum number of columns in supersaturated designs with

Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle .     

Characterizations of ( m,n )-Jordan Derivations and ( m,n )-Jordan Derivable Mappings on Some Algebras

Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A~2) = 2 mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every(m, n)-Jordan derivation with m = n from a C*-algebra into its Banach bimodule is zero. An additive mappingδ from R into M is called a(m, n)-Jordan derivable mapping at W in R if(m + n)δ(AB + BA) =2mδ(A)B + 2 mδ(B)A + 2 nAδ(B) + 2 nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left(right) separating set generated algebraically by all idempotents in A, then every(m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital(A, B)-bimodule and U = [A M N B] is a generalized matrix algebra, then every(m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.     

Birnbaum‐Saunders distribution: A review of models,analysis, and applications

Birnbaum and Saunders introduced a two‐parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix‐variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research.     

Infrared spectroscopy of closed s-shell gas-phase M+(N2O)n (M = Li,Al) ion-molecule complexes*

ABSTRACT

We present the results of a combined experimental and computational study of the structures of gas-phase M⁺(N₂O)_n (M?=?Li, Al) complexes. Infrared spectra were recorded in the region of the N₂O asymmetric (N?=?N) stretch using photodissociation spectroscopy employing the inert messenger technique. Unlike in our previous studies on M⁺(N₂O)_n (M?=?Cu, Ag, Au and M?=?Co, Rh, Ir) complexes, N– and O–bound isomers in this case are near isoenergetic and are not distinguished spectroscopically at this resolution. In the case of Li⁺ complexes, there is, however, evidence for the presence of bound N₂ moieties, indicating the presence of inserted, OLi⁺N₂(N₂O)_n–type structures. The weak N₂ band lies to the blue of the signature of molecularly N– and O–bound ligands and is well–reproduced in the simulated spectra of energetically low-lying structures computed from density functional theory. No such inserted isomers are observed in the case of Al⁺(N₂O)_n complexes whose infrared spectra can be understood on the basis of molecularly-bound N₂O ligands. The differences in M⁺(N₂O)_n structures observed for these closed–shell, ns², metal centres relative to other metal cations are discussed in terms of the likely bonding motifs.     

Synthesis and characterization of Co (III) salen complex immobilized on cobalt ferrite‐silica nanoparticle and their application in the synthesis of spirooxindoles

The preparation, characterization and catalytic application of Co (III) salen complex loaded on cobalt ferrite‐silica nanoparticle [CoFe₂O₄@SiO₂@ Co (III) salen complex] are described. Co (III) salen complex loaded on ferrite cobalt‐silica nanoparticles is characterized by transmission electron microscopy, scanning electron microscopy coupled with energy‐dispersive X‐ray, vibrating‐sample magnetometer and Fourier transform‐infrared analyses. The thermal stability of the material is also determined by thermal gravimetric analysis. An average crystallite size is determined from the full‐width at half‐maximum of the strongest reflection by using Scherrer's approximation by powder X‐ray diffractometry. The efficiency of CoFe₂O₄@SiO₂@Co (III) salen complex is investigated in the synthesis of spirooxindoles of malononitrile, various isatins with 1,3‐dicarbonyles. The nanocatalyst demonstrated excellent catalytic activity that gave the corresponding coupling products in good to excellent yields. Moreover, the recoverability and reusability of CoFe₂O₄@SiO₂@Co (III) salen complex is investigated where nanocatalyst could be recovered and reused at least five times without any appreciable decrease in activity and selectivity, which confirmed its high efficiency and high stability under the reaction conditions and during recycling stages.